What is a word/phrase to describe someone who thinks someone else is perfect? For instance, if parents think that their child can do no wrong, then they are . . .? (Not necessarily biased or partial, because it is not in comparison to anyone else)

I think idolizing is just perfect for this application. It gives just the right sense of the behavior being out of balance (where adoring seems like something any parent might naturally do) and doting seems to indicate that the child is still very young. Idolizing goes right on into adulthood!
– LynnjaminMar 1 '16 at 16:11

I upvoted this one before the question changed to take "awe" out. Changing the question necessarily changes the answer, too. I can't withdraw my vote without the answer changing, but it ought to let me do that because the question changed too, dammit.
– Monty HarderMar 2 '16 at 19:17

@Monty it ought to be noted that the question was rewritten by someone other than the original asker, in a matter that, as you noted, radically changes the question. While the editors interpretation of the original intent is a valid interpretation, it is far from the only valid interpretation. I'm not interested in starting a rollback war, but I'm also not going to rewrite or delete this answer to reflect a revision that I feel has dubious value.
– LessPop_MoreFizzMar 3 '16 at 1:55

Doting is good, but it is almost always used only in the specific sense of describing the attitude of an indulgent parent or relative to a child (admittedly the specific example the OP gave)
– Charl EMar 1 '16 at 15:52

I would argue that although that is its most common usage, it doesn't have to be limited to that, but it's a point to keep in mind nonetheless.
– John CliffordMar 1 '16 at 15:53

It probably doesn't have to be limited to that, but personally it would seem weird to me if I heard it used in any other context.
– Anthony GristMar 1 '16 at 15:55

Dotage is giving things to someone that they want, not thinking that they are flawless. Nursing, in a sense.
– The NateMar 2 '16 at 20:06

@TheNate Dotage is a noun, meaning "​old ​age, ​especially with some ​loss of ​mental ​ability" (Cambridge dictionary). It's nothing to do with giving things to someone that they want, and it doesn't mean the same thing as doting. Furthermore, the word "dote" literally means "be extremely and uncritically fond of." or some variation of that in most dictionaries, meaning it is 100% what the OP asked for.
– John CliffordMar 2 '16 at 20:16

I can be in awe of someone I hate. I can respect and admire someone's ability while still considering them to be the spawn of Satan. On the flip side of that, I can adore someone while still recognizing that they are far from perfect or deeply flawed.
– Darrel HoffmanMar 1 '16 at 19:44

I think Idolizing is probably the best fit, but it seems that you're looking to place an adjective/title on the people that perform this behavior then it would be more appropriate to say that they are idolizers. Here are a couple other options in the same neighborhood:

Venerator - A person that regards or treats with reverence; revere.

Fanatics - could also be another consideration as that has an implied sense of blindness to negative qualities

Orwell was indeed unsociable, anti-feminist and homophobic, but only ambiguously anti-Semitic, and by no means such a dewy-eyed idealiser of the plebs as some have imagined.

(def and example from ODO).

It doesn't work that well if you want an adjective, but you could use a participle:

A cognitive theory perspective emphasizes that idealizing parents may cause the child to develop an overactive view of the self that includes inflated beliefs of personal uniqueness and self-importance. In this approach to child rearing, the parents may systematically deny or distort negative feedback to their child.